PRESIDENTIAL ADDRESS. 699 



These figures show that a more conservative system of financing the railways 

 might have been adopted in the earlier days with advantage. If when the receipts 

 per train-mile were larger, a proportion of the revenue had been used annually 

 for the construction of new works and for the provision of new rolling-stock 

 instead of raising fresh capital for everything in the nature of an addition to the 

 railway, the companies would to-day have been in a position to regard with 

 equanimity the increasing cost of working. 



It is too late in the day to recover such a strong financial position, but even 

 now on many lines a larger proportion of the revenue could be sunk in the line 

 with great ultimate advantage to the financial position. 



The Problem of the Locomotive Department. 



During the last twenty years the demand on the locomotive has steadily 

 increased. The demand has been met, though with increasing difficulty, owing to 

 the constructive limitations imposed by the gauge. The transference of a train 

 from one place to another requires that work should be done continuously by the 

 locomotive against the tractive resistance. The size of the locomotive is deter- 

 mined by the rate at which this work is to be done. If T represents the tractive 

 resistance at any instant, and V the speed of the train, then the rate at which 

 work is done is expressed by the product TV. The pull exerted by the loco- 

 motive must never be less than the resistance of the whole train considered as a 

 dead load on the worst gradient and curve combination on the road, and it can 

 never be greater than about one-quarter of the total weight on the coupled wheels 

 of the engine. 



Again, the tractive pull of the engine may be analysed into two parts — one 

 the pull exerted to increase the speed of the train, the other the pull required to 

 maintain the speed when once it has been reached. For an express train the 

 number of seconds required to attain the journey speed is so small a fraction of 

 the total time interval between the stops that the question of acceleration is not 

 one of much importance. But for a local service where stops are frequent the 

 time required to attain the journey-speed from rest is so large a fraction of the 

 time between stops that this consideration dominates the design of the locomotive 

 and, in fact, makes it desirable to substitute the electric motor for the locomotive 

 in many cases. 



An accurate estimate of the rate at which work must be done to run a stated 

 service can only be made if there are given the weight of the vehicles in the 

 train, tbe weight of the engine, the kind of stock composing the train, the speed 

 and acceleration required at each point of the journey and a section of the road ; 

 and, in addition to this, allowance must be made for weather conditions. 



A general idea of the problem can, however, be obtained by omitting the 

 consideration of acceleration, gradients, and the unknown factor of weather con- 

 ditions, considering only the rate at which work must be done to draw a given 

 load at a given speed on the level. Even thus simplified the problem can be 

 solved only approximately, because, although the tractive resistance of a train 

 as a whole is a function of the speed, the tractive resistance per ton of load of 

 the vehicles and per ton of load of the engine differ both in absolute value and 

 in their rates of change for a stated speed, and, further, the ratio between the 

 weight of the vehicles and the weight of the engine is a very variable quantity. 



For our purpose, however, it will be sufficiently accurate to assume that the 

 resistance of the whole h - ain, expressed in pounds per ton, is given by the 

 formula 



T = 5J+ — 

 256 



It follows that the horse-power which must be developed at the driving-wheels 

 to maintain a speed of V miles per hour on the level with a train weighing 

 W tons is 



H p= w a+ vm 



)70 96.000/ 



